An empty relative density bottle weighs 40g. The bottle weighs 80g when filled with methylated spirit. And 90g when filled with water. Find the...

Hello!

I think that the volumes of spirit and water were the same, and probably equal to the inner volume of a bottle. Denote this volume as `V_b.`

A volume `V,` a mass `m` and a density `rho` are bounded by the relation `rho=m/V.` In particular,

`rho_s=m_s/V_b` and `rho_w=m_w/V_b,`

where `rho_s` is the density of spirit, `m_s` is its mass, `rho_w` is the density of water and `m_w` is its mass. Denote also the mass...

Hello!

I think that the volumes of spirit and water were the same, and probably equal to the inner volume of a bottle. Denote this volume as `V_b.`

A volume `V,` a mass `m` and a density `rho` are bounded by the relation `rho=m/V.` In particular,

`rho_s=m_s/V_b` and `rho_w=m_w/V_b,`

where `rho_s` is the density of spirit, `m_s` is its mass, `rho_w` is the density of water and `m_w` is its mass. Denote also the mass of a bottle as `m_b.`

The masses are actually known: `m_s=80g-m_b=40g` and `m_w=90g-m_b=50g.`

So we have two (linear) equations and two unknowns, `rho_s` and `V_b.` From the second equation `V_b=m_w/rho_w,` substitute it into the first equation and obtain:

`rho_s=m_s/V_b=(m_s/m_w)*rho_w.`

We can use any units for `rho_w` here because `m_s/m_w` is dimensionless. Therefore:

`p_s` = (40/50)*1000 = 800 `((kg)/m^3)`.